A variety of structures resonate with a fundamental frequency often combined with a plurality of other frequencies that make detection and analysis of the fundamental frequency problematic. Furthermore, many structures resonant for only a short period of time. A particular example of a resonant structure is a drum.
In one example, a drum consists of a hollow cylinder with a circular membrane clamped to either or both ends of the cylinder. A circular membrane that is suspended under tension at its outer perimeter is capable of several modes of vibration including circular symmetric and angular modes. The circular modes are described by a series of first-order Bessel functions for example and are therefore not harmonically related. The frequency of vibration depends, in part, on the radius, tension and density of the membrane. A cylindrical air column also resonates with the frequency of resonance depending on the length of the drum and the speed of sound and whether or not the ends of the cylinder are open or closed. Furthermore, the combination of a cylindrical shell and cylindrical membranes resonates as a system at a variety of frequencies that depend on a number of parameters, such as the dimensions of the drum, the tension and density of the drum-heads and the composition of the shell.
In one example, a drum-head is held by a metal or wooden hoop that is attached to a drum shell with several adjustable tension screws. The tension of the drum-head is determined by the force exerted by the tension screws. Tuning involves adjusting the tension screws to achieve a uniform pitch over a drum-head. When the pitch is uniform around the perimeter of the drum, the drum-head is considered to be “cleared” or “in tune with itself.” In addition to being in tune with itself, each drum-head needs to be adjusted to a pitch that produces the desired overall sound. It is sometimes desirable to tune each head separately with the other held damped to prevent vibration.
Striking a drum produces a percussive sound that's shorter in duration than any non-percussive musical instrument. The time-domain response of a typical drum, consists of an oscillatory signal with an abrupt onset followed by a short, approximately exponential, decay. Air pressure acting on the large area of the drum-head limits the duration of the sound. A vibrating string on the other hand has a much smaller area than a drum-head and vibrates much longer in comparison.
Tuning a set of drums poses additional challenges for musician. Some drummers tune their drums to a musical chord such as a major chord. Other drummers tune their drums to relative tonic intervals such as thirds or fifths, and still others tune by ear to something suiting their musical taste. The choice of specific drum pitches sometimes depends on the type of music being played. A drum-set might be tuned higher for jazz than for rock, for example, or it might be tuned open to resonate for a live performance or tight for a recording. Tuning also depends on the size and type of drum. A larger diameter drum is usually tuned lower than a smaller diameter drum. Often drummers attempt to copy the pitches used by other drummers from recordings or from memory. In general, the desired tuning of a drum-set depends on the particular sound the drummer is looking for.
A drum produces a unique sound when its head is struck resulting from the resonance of the vibrating heads in conjunction with the shell of the drum. Striking a drum excites several rapidly-decaying, non-harmonic modes of vibration resulting in a short, complex burst of sound. Drum tuning, by adjustment of a drum-head tension, to control pitch, tone and timber is essential in establishing a pleasing drum sound. Tuning any musical instrument involves playing a note, measuring or comparing the pitch of the note to some reference and adjusting the instrument's pitch until it conforms to the reference. However, assessing the pitch of a drum is complicated by the short duration and multiple non-harmonic resonances comprising its sound. Melodic instruments, on the other hand, produce continuous, periodic (harmonic) sounds with easy to measure pitch and are therefore much simpler to tune than a drum.
Drum tuning is typically done by ear, which is an art subject to the skill and taste of an individual musician. In addition, tuning by ear is inaccurate and has poor repeatability of results. Moreover, it is increasingly difficult to tune by ear when tuning a drum-set where each drum typically is tuned to a different pitch or to tune the drum-set to a variety of popular drum-set sounds varying based on style of music or the acoustic properties of the physical environment within which the drum-set will be used.
Existing tuners for melodic instruments such as guitars and pianos are unsuitable for drum or drum-set tuning. They require a sustained tone duration that is longer than the duration of a drum sound and only operate correctly on a periodic signal consisting of a single fundamental and associated harmonics, not on the transient sound produced by a drum. Drums typically create overtones unlike harmonics that are more easily distinguished from the fundamental frequency. Overtones are typically related to the fundamental frequency by a product of it π (pi), being related to the area and circumference of the drum-head.
Mechanical tuning devices exist that measure the tension of the drum-head by measuring the deflection of the head for a given force but do not measure the pitch produced by a drum and thus suffer from a variety of inaccuracies due to drum skin thickness and temperature variations for example.